Permutations with forbidden subsequences and nonseparable planar maps

The goal of the present work is to connect combinatorially a family of maps to a family of permutations with forbidden subsequences. We obtain a generating tree of nonseparable planar rooted maps and show that this tree is the generating tree of a family of permutations. The distribution of these permutations is then obtained. Finally, the different steps leading to the combinatorial proof of West's conjecture are listed.